Umayyad Square is a large open space at the center of a major crossroads, less than a mile from the presidential palace. A year ago, it was the scene of a large demonstration in support of Assad.

Around the square are the state television offices, the army’s general staff headquarters, university buildings, the Sheraton hotel, and the Damascus Opera House, a showpiece of the commitment to high culture that Assad liked to project and the venue for his rare public speech in January.

The rebellious Free Syrian Army took responsibility for Monday’s attack, saying it used rocket launchers aimed at the state broadcaster.

Syria’s state news agency, SANA, said six people were killed and dozens injured when a mortar round struck close to the opera house in the high-security zone. Other state media put the number of deaths at two.

The military struck back, shelling rebel positions from Mount Qasioun, where the presidential palace overlooks the city. It was hard to pinpoint the position of the rebel mortars.

Reuters reported that insurgents were firing from Kafr Souseh, a southwestern area where rebels have recently attacked security buildings, which is less than a mile from Umayyad Square.

In a separate development, American and foreign officials said the United States is training secular Syrian fighters in Jordan in a bid to bolster forces battling Assad’s regime and stem the influence of Islamist radicals among the country’s opposition, the Associated Press reported Monday.

The training has been conducted for several months now in an unspecified location, concentrating largely on Sunnis and tribal Bedouins who formerly served as members of the Syrian army, officials said. The forces are not members of the Free Syrian Army.

The operation is being run by US intelligence, officials said. Although the United States is providing only nonlethal aid at this point, the CIA has been helping Arab governments and Turkey provide military aid to the opposition fighters.

The rebel mortar shelling in central areas of Damascus panicked residents who fear that the capital, which has largely been spared the urban warfare that has devastated Syria’s other major cities, could be next.

But so far, the government has managed to keep rebels from pushing deep into the capital.

After mortar shells fell Sunday and Monday near the downtown Damascus hotel that the United Nations uses as its Syria headquarters, the world body told its 800 Syrian employees to work from home for the time being and evacuated half of its 100 non-Syrian employees to Beirut or Cairo, according to Martin Nesirky, the spokesman for Secretary-General Ban Ki-Moon.

Nesirky said the steps were temporary and should not affect the distribution of humanitarian aid coordinated by the United Nations in Syria.

The new fighting came as the opposition reported that a senior rebel leader had been wounded in an explosion in Mayadeen, in the province of Deir el-Zour in eastern Syria, where rebels have seized large amounts of territory.

The blast hit Colonel Riad al-Asaad, one of the most prominent defectors from the Syrian military and a top figure in the Free Syrian Army, the umbrella group that has attempted to unify rebels under one command.

He has been less prominent lately after General Salim Idriss was named head of the Free Syrian Army’s unified command, which has also struggled to unite fighters who largely rely on their individual contacts to scrounge up weapons. But he still occasionally visits rebel groups inside the country.

It was unclear who was responsible for the explosion that wounded Asaad; some fighters have expressed worry that there could be conflict between battalions nominally loyal to the Western-backed Free Syrian Army and those fighting under the banner of Islamist groups such as the Nusra Front.

Malek al-Kurdi, the deputy commander of the Free Syrian Army, accused the Syrian government of being involved in the attack.

He said in a telephone interview that an explosive device attached to Asaad’s car detonated after he visited a school in the Mayadeen-Deir el-Zour area, parts of which are still under government control.

He said Asaad, whose right leg was amputated below the knee, was first treated in a field hospital before being transported to Turkey.

Mouaz al-Khatib, the president of the opposition coalition, reported on his Facebook page that Asaad had been transported to safety with the help of other rebel groups — a statement that appeared to suggest he had not been targeted by fellow fighters.

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